The driver refused to load or to install, and in Device Manager, the card is shown as an unknown sound card or as "C-Media Oxygen audio device".
Putting the card into another slot or another computer does not help.

This happens when the EEPROM on the card gets overwritten.
(This EEPROM stores the PCI subsystem vendor and product IDs;
when it gets overwritten, the main chip cannot read the subsystem IDs
and uses a default ID (13F6:8788) which is not recognized by the Xonar driver.)

To reliably detect whether the EEPROM was overwritten,
go into Device Manager, show the properties page of the device,
go to the "Details" tab, and select the property "Hardware IDs",
and look at the values after "SUBSYS_":

The exact cause is unknown.
It seems that the problem occurs only with certain computers or motherboards,
and after booting from a CD (i.e., (re)installation of an operating system, or using a live CD).